FFXI Equations/Statistics Thread

Probly a stupid question, but in those formulas... what do you mean by "floor" >_>...

Bad, but stylishly bad. :p

/derail off :p

Floor = round down
Ceiling = round up

I think, correct me if i'm wrong please!

oh, that would make sense... since everything is rounded down in xi, no?

Correct, and I've seen some other game equations where it is the opposite.

Yes, this is true.

Though I didn't use this notation in my post, I just said "since this value is an integer, you round down.

Not everything is, no, however most things are floored to their lowest value. It isn't rounding, it's dropping the decimals completely in most circumstances, similar to truncation. Actually, basically the same thing.

It was just me being stupid :3

in Prothescar's post it looked like floor was a variable to me, I'm obviously not a math person.



oh, ok :x lol

Also Dabackpack, there is a ~60,000 character limit (including spaces) in posts I think (can vary depending on what bbcode you're using).

I'm not sure if you are going to hit that limit or not, I've only done it in two topics ever.

Difference between actually rounding and flooring, the floor will always go to the closest, lowest number. 'Tis why it's called flooring. Same with Ceiling except it's higher number.

Essentially it's data loss due to converting from one datatype that can handle decimals to one that doesn't.

Is using an integer rather than an double data type really saving them that much calculation time? It's just 4 bytes vs 8.

PS2 limitations

That's twice as many! And to be honest, MOST players wont realize what they are missing because the dropped decimals are usually negligible.

BUT GAIZ, THE DEVS SAID PS2 LIMITATIONS WUZ UH MYTHHHHHHH!!!!

I'm at 4k now, but that's after explaining important aspects of physical damage which can be partly reused for WS damage

The usage of ints over doubles I think really was kind of a dumb move, granted we don't know whether or not ps2 limitations was/is a factor (probably was, always will be apparently).

The information to be processed for these calculations goes by in a fraction of a second, and to use doubles would probably boost memory usage by a negligible amount.

The information then is discarded after the results are narrowed into an int for display (ws damage), or probably stored within a variable, where in which case there's little to no difference between the handling of the 2. (Hell they use doubles for stuff nowadays anyways, hi2u Mekira Meikogai.)

Either the dev team really really really wanted to prioritize speed of calculation (which might be understandable given the processors of 2003), or started making the system in ints, went OH ***, and just worked with it because they didn't feel like CTRL + Zing.

tl;dr Disregard ints, acquire doubles

No other contributions, but cash credit, general debit.

Getting there. Please let me know if I'm giving false information.

Thanks all!

Heh, needs a meme pic to go with it.
I figured they'd leave this crap behind when games got off of the nes. My only real complaint is that fractional improvements often give you no boost and you end up with a lot of plateaus in calcs as well as that it's just a pain in the arse to figure out formulas when you are flooring at random points. I'm not all that great at complex multilevel math so putting truncations in it just means that I have to let other people do it.

I'm writing you up something silly, lolololol.

The Diminishing Returns of Double Attack

We're going to take a special approach to discussing double attack calculations, which you don't see very often because most of the people who discuss FFXI equations are math people, and as such, they inherently understand how things work without having to think about the actual derivation of formulae. I notice that people seem to get confused on what adding an extra point of double attack actually does for them, so I will try to explain it in this novel way. In particular, this approach is based on the combinatorial model. Now, I don't always use combinatorial models, but when I do, I like to use rappers. So without further ado:

Assume we have 100 up-and-coming rappers signed to our label, "Jamtotto." All of them are wearing the signature Jamtotto t-shirt, which is a plain shirt printed with a lowercase letter "j."

*In this case, each rapper represents a single melee attack round (or in the case of dual wielding, per melee swing). The "j" on their shirts represents your average melee damage per hit. So, if we put all the rappers together, it's easy to see that per 100 attack rounds, we're doing, on average, 100j damage.
*Since each rapper has exactly one "j" printed on their shirt, this represents the situation where double attack is currently at 0%.
*To model double attack, for every 1% of double attack we add to a particular situation, we will simply print an additional "j" on a single rapper's shirt.
*To calculate % increases in DPS, we will use the total damage dealt per 100 attacks rounds, which is simply the total number of "j"s that appear on our rappers' shirts multiplied by "j". For example, if we have 50% double attack, then 50 of our rappers will have 2 "j"s on their shirts and 50 will have a single "j". The total number of "j"s is 50*2 + 50*1 = 150, so we deal a total of 150j damage.

All right! Now that we've gotten the basic "rules of the game" out of the way, we can start doing some calculations.

1.) Assume we start with 0% double attack (100j total damage per 100 attack rounds). How much does our DPS increase if we add 1% of double attack?

Well, we simply take a sharpie and draw an extra "j" on the first rapper. Counting up the rapper's shirts, we now have 101 "j"s, and as such we're now dealing 101j damage per 100 attack rounds.
But wait! We need to calculate the % increase!

First, we calculate the difference in damage which is really EASY to calulate:

Difference in Damage (D) = (total damage after changing the double attack %) - (total damage before changing the double attack %)

So in this case, D = 101j - 100j = j, meaning after adding 1% of double attack, we deal on average, j more damage than before adding 1% of double attack. To calculate the percent damage increase, we simply divide the difference in damage by the original total damage and multiply by 100. In this case:

(j / 100j) * 100 = 0.01 * 100 = 1%

Our total damage increased by 1% (as long as adding that double attack didn't change the amount of haste you had, this is also equivalent to the % Increase in DPS since the time units would cancel out), which is what you'd intuitively expect from adding 1% of double attack. Unfortunately, however, the result is only intuitive if we started with 0% doible attack.


2.) Now, assume we start with 50% double attack (150j total damage per 100 attack rounds) and add 1% double attack. How much does our DPS increase now?

Assuming we don't get shanked after drawing on the 51st rapper's shirt, we can count up the "j"s. We now have 151 of them, so we're dealing 151j damage. So we calcualte the difference in damage:

D = 151j - 150j = j

And use this to find the percent damage increase, just like we did before except now we divide by 150j since we started with 50 rappers having double "j"s:

(j / 150j) * 100 = 1/150 * 100 = 0.0067 * 100 = 0.67%

This time, our total damage only increased by 0.67% - substantially less than when we started with 0% double attack.

From this, we can conclude the following:

1.) Double attack has Diminishing Returns, meaning that the more you have of it to start with, the less you benefit from adding more. Note that diminishng returns does not mean that at some point adding a single point of double attack will start to decrease your DPS, on which point some people get confused.
2.) We can calculate the damage increase from adding double attack as follows:

% Damage Increase = (% DA added) / ( 100 + % orginal DA ) * 100

3.) Rappers don't shank you when you draw on their shirts.
4.) It's very easy to extend this to triple or quadruple attack. You'd just add additional j's as needed. It's more complicated when you have double AND triple attack etc, because they take priority over each other and thus make the model a tad more complicated.

Good analogy :D
I didn't say something wrong, did I? :O

Nope, you were right, but I think concepts like "the less you gain by adding more" are not particularly intuitive and people greatly benefit from seeing how such a feat is accomplished.

Um.
Quick question.
Are you by any chance planning on making a section for the various formulas of the correlation between haste and time to proc? :(

Already on it. Also modelling with rappers.

Agreed, it seems quite a few have misconceptions about DA.

I'll add the stuff you all are posting to the OP when I get around to it. I can link to your posts if I run low on space right?

Funny you should say this, I was seriously considering adding that to my short haste section. No lie.

Consider it done.

Player TP Gain should have a section.

Dual Wield needs more

Also worth mentioned that other factors such as DMG, Attack, MAB, Defense, etc have decreasing returns to go along with DA/TA/QA.

And you can model it in the same exact way, really.